1 Answer
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According to the TF2 wiki on Obtaining Scout Achievements, mini-sentries do count. The full text from that page is quoted below, with emphasis added:

Gun Down

Destroy an active sentry gun using your pistol.

Difficulty: Medium

How to obtain: The safest way to take out a Sentry Gun with your Pistol is to snipe an exposed section from long-range, especially if it is unattended. A more risky method would be to attack as you would with the Scattergun, circle strafing around the Sentry Gun so it does not lock onto you. You can get assistance from other classes as long as you land the finishing hit. Combat Mini-Sentry Guns deployed by Engineers with the Gunslinger are particularly easy to destroy. This achievement can be obtained by using the Shortstop as well.